Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

dratum A H eidem rectangulo NIO eſt æquale, cum ſit NIO parallela ad A C, & per I punctum medium baſis E G ducta, & c. ergo, & quadra-
tum M I ipſi A H, ſeu linea M I lineæ A H æqualis erit, ſed Ellipſis E M
G ad circulum A L C eſt vt rectangulum ſub G I, & I M ad quadratum ex A H, vel vt linea G I ad A H (ob communem altitudinem M I) vel
ſumptis duplis, vt E G ad A C, ergo baſis portionis ſolidę E F G, ad baſim
portionis ſolidę A B C, eſt vt E G baſis Canonis E F G, ad A C baſim Ca-
nonis A B C; verùm vt E G ad A C, ita eſt reciprocè altitudo Canonis A B C ad altitudinem Canonis E F G (cum ipſi Canones ęquales facti ſint)
atque Canonum altitudines eædem ſunt cum altitudinibus ſolidarum por- tionum, vnde baſis E M G ad baſim A L C erit reciprocè, vt altitudo ſoli-
dæ portionis A B C ad altitudinem ſolidæ E F G: hæ autem portiones ſunt
ſolida Acuminata proportionalia, eò quod ipſarum Canones ſint æquales, atque baſes altitudinibus ſunt reciprocæ, ergo huiuſmodi portiones ſolidæ
A B C, E F G ſunt æquales. Quod demonſtrandum erat.

340.1.

12. ibid.
16. Vnd.
Elem.
3. ibid.
19. ibid.
77. h.
ex 6. Ar-
chim. de
Conoid.
65. h.
0295-01
3. Schol.
69. h.
Coroll.
70 h.
74. h.

Sed hoc idem, tribus proximè præcedentibus propoſitionibus omisſis,
ſuper nouo diagrammate ſic oſtendere conabimur

341. ALITER.

SIt Conus rectus, vt in prima figura, vel aliud quodcunque prædictorum
ſolidorum, vt in ſecunda, circa axim A B, & ſectio per axim ſit E A
D, quæ genitrix erit dati ſolidi, à qua demptæ ſint duæ quælibet portio- nes planæ æquales C A D, E A F, quarum baſes ſint C D, E F, & per ip-
ſas ducantur piana ſecantia data ſolida, & ad ipſum planum per axem E A
D erecta, circulos, vel Ellipſes E O F, C P D deſcribentia (quarum ma- iores axes in Cono, Conoide Parabolico, Hyperbolico, & Sphæroide ob-

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